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We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in…
Non-blind image deblurring is typically formulated as a linear least-squares problem regularized by natural priors on the corresponding sharp picture's gradients, which can be solved, for example, using a half-quadratic splitting method…
Next-generation radio interferometric telescopes will exhibit non-coplanar baseline configurations and wide field-of-views, inducing a w-modulation of the sky image, which in turn induces the spread spectrum effect. We revisit the impact of…
The inverse problem of multilayer thin-film optical coatings design represents a complex combinatorial-continuous optimization challenge. We present PRISM (Position-encoded Regressive Inverse Spectral Model), a unified decoder-only…
Computed tomography is widely used to examine internal structures in a non-destructive manner. To obtain high-quality reconstructions, one typically has to acquire a densely sampled trajectory to avoid angular undersampling. However, many…
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…
Compressive sensing is a method to recover the original image from undersampled measurements. In order to overcome the ill-posedness of this inverse problem, image priors are used such as sparsity in the wavelet domain, minimum…
Over the brief time intervals available for processing retinal output, roughly 50 to 300 msec, the number of extra spikes generated by individual ganglion cells can be quite variable. Here, computer-generated spike trains were used to…
Two of the main challenges of image restoration in real-world scenarios are the accurate characterization of an image prior and the precise modeling of the image degradation operator. Pre-trained diffusion models have been very successfully…
Contrast enhancement and noise removal are coupled problems for low-light image enhancement. The existing Retinex based methods do not take the coupling relation into consideration, resulting in under or over-smoothing of the enhanced…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
Decoding stimulus images from fMRI signals has advanced with pre-trained generative models. However, existing methods struggle with cross-subject mappings due to cognitive variability and subject-specific differences. This challenge arises…
Parallel imaging is a commonly used technique to accelerate magnetic resonance imaging (MRI) data acquisition. Mathematically, parallel MRI reconstruction can be formulated as an inverse problem relating the sparsely sampled k-space…
Understanding how the brain encodes visual information is a central challenge in neuroscience and machine learning. A promising approach is to reconstruct visual stimuli, essentially images, from functional Magnetic Resonance Imaging (fMRI)…
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…
Barcodes are ubiquitous and have been used in most of critical daily activities for decades. However, most of traditional decoders require well-founded barcode under a relatively standard condition. While wilder conditioned barcodes such as…